Brita E. A. Nucinkis

On algebraic and geometric dimensions for groups with torsion

We argue that the geometric dimension of a discrete group G ought to be defined to be the minimal dimension of a model for the universal proper G-space rather than the minimal dimension of a model for the universal free G-space. For torsion-free groups, these two quantities are equal, but the new quantity can be finite for groups containing torsion whereas the old one cannot. There is an analogue of cohomological dimension (defined in terms of Bredon cohomology) for which analogues of the Eilenberg-Ganea and Stalling-Swan theorems (due to W. Lueck and M. J. Dunwoody respectively) hold. We show that some groups constructed by M. Bestvina and M. Davis provide counterexamples to the analogue of the Eilenberg-Ganea conjecture.

Cohomological finiteness conditions for elementary amenable groups

Abstract It is proved that every elementary amenable group of type FP∞ admits a cocompact classifying space for proper actions.

Every CW-complex is a classifying space for proper bundles

Abstract We prove that, up to homotopy equivalence, every connected CW-complex is the quotient of a contractible complex by a proper action of a discrete group, and that every CW-complex is the quotient of an aspherical complex by an action of a group of order two.

Complete cohomology for arbitrary rings using injectives

We will develop a complete cohomology theory, which vanishes on injectives and give necessary and sufficient conditions for it to be equivalent to the generalized Tate cohomology theory developed by Mislin, Benson and Carlson and Vogel.

On Bredon homology of elementary amenable groups

We show that for elementary amenable groups the Hirsch length is equal to the Bredon homological dimension. This also implies that countable elementary amenable groups admit a finite-dimensional model for

COHOMOLOGICAL FINITENESS PROPERTIES OF THE BRIN-THOMPSON-HIGMAN GROUPS 2V AND 3V

\underbar{EG}

BREDON COHOMOLOGICAL FINITENESS CONDITIONS FOR GENERALISATIONS OF THOMPSON GROUPS

of dimension less than or equal to the Hirsch length plus one. Some remarks on groups of type

Cohomology relative to a G-set and finiteness conditions

FP_\infty

Cohomological finiteness conditions in Bredon cohomology

are also made.

Virtually soluble groups of type FP

We show that Brins generalisations 2V and 3V of the Thompson-Higman group V are of type FP1. Our methods also give a new proof that both groups are nitely presented.